Near-Optimal Streaming Approximation for Max-DICUT in Sublinear Space Using Two Passes

The Max-DICUT problem has emerged as a canonical problem for understanding the approximability of constraint satisfaction problems in the streaming model. A seminal result of Kapralov and Krachun [STOC 2019] shows that it is impossible to beat 1/2-approximation for Max-DICUT in sublinear space in the single-pass streaming setting, even on bounded-degree graphs. In a recent work, Saxena, Singer, Sudan, and Velusamy [SODA 2025] prove that the above lower bound is tight by giving a single-pass algorithm for bounded-degree graphs that achieves (1/2-ε)-approximation in sublinear space, for every constant ε > 0. For arbitrary graphs of unbounded degree, they give an O(1/ε)-pass O(log n) space algorithm. Their work left open the question of obtaining 1/2-approximation for arbitrary graphs in the single-pass setting in sublinear space. We make progress towards this question and give a two-pass algorithm that achieves (1/2-ε)-approximation in sublinear space, for every constant ε > 0.